scholarly journals Instability of a viscous interface under horizontal quasi-periodic oscillation

2019 ◽  
Vol 286 ◽  
pp. 07010
Author(s):  
M. Assoul ◽  
A. El Jaouahiry ◽  
M. Echchadli ◽  
S. Aniss
Keyword(s):  
Frequency Ratio ◽  
Linear Problem ◽  
Periodic Oscillation ◽  
Immiscible Fluids ◽  
Kutta Method ◽  
Periodic Excitation ◽  
Helmholtz Instability ◽  
Quasi Periodic Oscillation ◽  
Runge Kutta Method ◽  
Parametric Resonances

We study the linear stability of two superposed layers of viscous, immiscible fluids of different densities. The whole system is subject to horizontal quasi-periodic oscillation with two incommensurates frequencies ω1 and ω2. The spectral method and Floquet’s theory combined with Runge-Kutta method are used to solve numericelly the linear problem. We analyse the influence of the frequencies ratio$ \omega = {{{\omega _1}} \over {{\omega _2}}} $, on the mariginal stability. The numerical solution shows that the quasi-periodic excitation has a stabilizing or a destabilizing effect on the Kelvin-Helmholtz instability as well as in the parametric resonances depending on the frequency ratio and the amplitudes ratio $ \alpha = {{{\alpha _2}} \over {{\alpha _1}}} $.

scholarly journals Influence of Quasi-Periodic Oscillation of Atmospheric Variables on Radiation Fog over A Mountainous Region of Korea

Atmosphere ◽  
2020 ◽  
Vol 11 (3) ◽  
pp. 230
Author(s):  
Inyeob La ◽  
Seong Soo Yum ◽  
Ismail Gultepe ◽  
Jae Min Yeom ◽  
Jae In Song ◽  
...  
Keyword(s):  
Periodic Oscillation ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Simultaneous Increase ◽  
Mountainous Region ◽  
Helmholtz Instability ◽  
Radiation Fog ◽  
Quasi Periodic Oscillation ◽  
Time Frequency ◽  
Atmospheric Variables

To enhance our understanding of fog processes over complex terrain, various fog events that occurred during the International Collaborative Experiments for Pyeongchang 2018 Winter Olympics and Paralympics (ICE-POP) campaign were selected. Investigation of thermodynamic, dynamic, and microphysical conditions within fog layers affected by quasi-periodic oscillation of atmospheric variables was conducted using observations from a Fog Monitor-120 (FM-120) and other in-situ meteorological instruments. A total of nine radiation fog cases that occurred in the autumn and winter seasons during the campaign over the mountainous region of Pyeongchang, Korea were selected. The wavelet analysis was used to study quasi-period oscillations of dynamic, microphysical, and thermodynamic variables. By decomposing the time series into the time-frequency space, we can determine both dominant periods and how these dominant periods change in time. Quasi-period oscillations of liquid water content (LWC), pressure, temperature, and horizontal/vertical velocity, which have periods of 15–40 min, were observed during the fog formation stages. We hypothesize that these quasi-periodic oscillations were induced by Kelvin–Helmholtz instability. The results suggest that Kelvin–Helmholtz instability events near the surface can be explained by an increase in the vertical shear of horizontal wind and by a simultaneous increase in wind speed when fog forms. In the mature stages, fluctuations of the variables did not appear near the surface anymore.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

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